Consider a region inside which, there are various types of charges but the total charge is zero. At points outside the region

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The electric field is necessarily zero.

The electric field will be only due to the dipole moment of the charge distribution only.

The electric field due to charges inside the region is inversely proportional to $r^{3}$ , for large $r$ (distance from origin)

The work done to move a charged particle along a closed path, away from the region will not be zero.

answer is C.

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Detailed Solution

When there are various types of charges in a region, but the total charge is zero, the region can be supposed to contain a number of electric dipoles. Therefore, at points outside the region, the dominant $electric field \propto \frac{1}{r^{3}}$ for large $r$ .

If there is a possibility external charges present near that point, So the electric field will be the net electric field due to the charges inside the region and also the external charges.

As all the forces are conservative in nature, the work done in moving a charged particle in a closed path will be zero.

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